Question

multiple choice question
find the magnitude of the sum of a 25.0 n force and a 34.0 n force, given that the angle between the two vectors when aligned tip to tail is 125°.
806 n
2.76×10³ n
52.5 n
28.4 n

Explanation:

Step1: Use the law of cosines

The formula for the magnitude \( R \) of the sum of two vectors \( A \) and \( B \) with an angle \( \theta \) between them (when aligned tip - to - tail) is \( R=\sqrt{A^{2}+B^{2}+2AB\cos\theta}\). Here \( A = 25.0\space N\), \( B=34.0\space N\), and \( \theta = 125^{\circ}\), so \(\cos\theta=\cos(180^{\circ}- 55^{\circ})=-\cos(55^{\circ})\approx - 0.5736\).

Step2: Substitute values into the formula

$$
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$$

Answer:

\(28.4\space N\)